I do appreciate any help, but I'm not at home at the moment so can't get the firmware revision, etc, on the home camera.
However, clearly the problem isn't wifi -- I can get to the camera fine on the LAN. My router model hasn't changed (it's an Asus running Tomato), nor have any of the settings. It's had the same DHCP-given IP address since it was installed over a year ago, and has worked fine, without an interruption I've noticed, since then.
So nothing in my configuration has changed, and it happened simultaneously for two cameras in two different locations, connected via two different ISPs.
I'll reboot my camera at home when I get back, and check the firmware version.